text:
\section{Introduction}
Quantum chaos explores the quantum-mechanical properties of systems whose classical counterparts exhibit deterministic chaos \cite{Stoeckmann,TOM94}. Most studies of quantum chaos in experimentally-accessible systems have focused on atoms \cite{Stoeckmann,atom_billiards,37} and semiconductor systems, in which electron confinement by potential energy barriers of various shapes generates chaotic classical trajectories.

Semiconductor superlattices, comprising a series of quantum wells, have been used to realize a fundamentally different regime of nonlinear dynamics, in which the effective classical Hamiltonian originates from an \emph{intrinsically quantum-mechanical} feature of the system: tunnel coupling of the wells to form energy bands, known as minibands \cite{FRO01,OSADA,FRO04,BAL2008,Green09}. When a bias voltage and tilted magnetic field are applied, the energy versus crystal momentum dispersion relation for the energy bands generates chaotic dynamics equivalent to those of a one-dimensional harmonic oscillator driven by a plane wave \cite{FRO01,FRO04,BAL2008,Green09}. Unusually, this system does not obey the KAM theorem \cite{ZAS91,ZAS2004,Luo04,Karney,Soskin09}, which means that chaos switches on and off abruptly at critical values of the applied fields. At the critical fields, the electron phase space is threaded by intricate web patterns, known as stochastic webs \cite{ZAS91,ZAS2004,Luo04,Karney,Soskin09}. These webs form a network of conduction channels, through which the electrons propagate in real space \cite{FRO01,OSADA,FRO04,BAL2008,Green09}. When the web is switched on, the electrons undergo chaotic diffusive motion along its filaments, thereby producing a sharp increase in the measured and calculated direct current \cite{FRO04,BAL2008} and increasing both the power and frequency of GHz/THz current oscillations by an order of magnitude \cite{Green09}. Consequently, chaotic semiclassical transport through energy bands provides a mechanism for controlling transport through periodic structures. In the absence of electron scattering, switching due to the formation and destruction of stochastic webs is extremely sensitive, due to the inherent instability of chaotic orbits, and would produce $\delta-$function peaks in the current-voltage characteristics. In real superlattices, though, the peaks are broadened by electron scattering. This limitation can, in principle, be overcome by using an analogous system comprising ultracold atoms moving through the energy bands of an optical lattice with a tilted harmonic trap \cite{Scott:02}.

Due to the formal similarity between Maxwell's equations and the Schr\"odinger equation \cite{Stoeckmann}, microwave and optical systems have been used to study the ray-wave correspondence, analogous to quantum chaos, for electromagnetic radiation. Much of this work has focused on electromagnetic billiards in which the radiation is confined in a quasi two-dimensional (2D) region of space, usually a cavity or dielectric block, whose boundary is shaped to create chaotic dynamics for light rays confined within the block. There has been considerable technological interest in such systems because, when used as a resonator for a micro laser, they can produce strongly focused emission whose power is orders of magnitude higher than obtained from traditional circular resonators \cite{Gmachl_1998, Lee_2004, Mekis_1995, Schwefel_2004, Nockel_1994}. Microwave systems have also been used to study the ray-wave correspondence in billiards, photonic crystals, and in a range of disordered dielectric media \cite{Stein_1995, Stockmann_1990, Kuhl_2000,StockNJP}.

In 2D photonic crystals \cite{shep1,PhysRevA.46.612}, ray dynamics related to the chaotic semiclassical motion of electrons in a superlattice miniband has been predicted when the lattice parameters, and hence the local refractive index, vary slowly with position \cite{crd, CTS}. Such structures offer major advantages over superlattices for studying, and potentially exploiting, chaotic band transport effects because they operate at room temperature and without an applied magnetic field. As a ray passes through the crystal, changes in the lattice parameters alter the local photonic band structure, in particular the shape and frequency range of the allowed bands. This exerts an effective \textquotedblleft force" on the ray \cite{pboawsl, crd}, whose trajectory can be determined by solving Hamilton's equations \cite{crd}, just like calculating the path of a classical particle subject to real forces. When the lattice parameters are chosen to approximate the potential landscape experienced by an electron in a superlattice with a tilted magnetic field, the ray paths share many characteristics of non-KAM chaos. In particular, they have a rich mixed stable-chaotic phase space structure \cite{crd}.

\begin{figure}[t]
\centerline{

   \includegraphics[width =\linewidth]{fig1.pdf}
  }
	\caption{Schematic diagram of the photonic crystal, which comprises two arrays of parallel dielectric sheets (gray)  intersecting at 90$^{\circ}$. Each sheet is of infinite area. The sheets are parallel to the $x$-$z$ or $y$-$z$ plane. The $x'$ and $y'$ axes are related to the $x$ and $y$ axes by a rotation of $\theta$ about the $z$ axis (inset).}
	\label{fig1}
\end{figure}

In this paper, we study the origin of mixed-stable-chaotic ray dynamics in spatially-modulated photonic crystals and how such dynamics depend on the parameters both of the crystal and the electromagnetic wave. We focus on two key aspects of the ray dynamics. Firstly, we consider how the spatial variation of the lattice parameters affects the range and dispersion of the allowed frequency bands and, hence, the ray trajectories obtained from Hamiltonian ray dynamics. Secondly, we analyze how the form of the ray trajectories, in real and phase space, depends on the frequency, $\omega$, of the electromagnetic wave. In contrast to previous work \cite{crd}, which considered ray dynamics at fixed frequency, we find that the location and extent of the stable and chaotic orbits depend strongly on $\omega$. By considering four critical points in the local Brillouin zone, we determine the loci of classically-allowed regions of the photonic crystal, where rays can propagate, and the corresponding forbidden regions that the rays cannot enter. Within the classically allowed regions, we identify additional \emph{dynamical} barriers, which are formed by localized stable orbits and are impenetrable to chaotic ray trajectories \cite{crd}. We show that as the ray propagates through the crystal, changes in the local bandstructure cause it to reach the band extrema (highest or lowest frequency within an allowed band), where Bragg reflection occurs. Together, Bragg reflection and the action of the dynamical barriers limit the spatial region in which a ray moves, and drive many ray paths chaotic. As $\omega$ increases, a single region of chaos splits into two distinct chaotic seas separated by a dynamical barrier. Further increasing $\omega$ suppresses chaos in one of these two regions, thereby deactivating the dynamical barrier and its effect on ray transport.

The structure of the paper is as follows. In Section \ref{sec:The structure of the crystal}, we define the crystal structure and consider the frequency-versus Bloch wavevector dispersion relations for the allowed frequency bands in which electromagnetic radiation can propagate through the crystal. Next, in Section \ref{sec:The ray tracing} we introduce the semiclassical (Hamiltonian) equations of ray motion and consider, qualitatively, how the shape of the dispersion relations influences the ray trajectories, in particular whether they are open or closed. In Section \ref{sec:The shape of the ray paths}, we consider the spatial regions of the crystal in which the rays propagate and show how the shapes of these regions, and the orbits themselves, are determined by the form of the dispersion relations and the photonic crystal structure. In Section \ref{sec:Dynamical Barriers}, we demonstrate the existence and influence of dynamical barriers, which originate from islands of stability within a chaotic sea rather than from a classically forbidden region of high potential energy. In particular, we show that these dynamical barrriers can control the transmission of electromagnetic waves through the photonic crystal. In Section \ref{sec:experiment}, we discuss possible routes to the experimental realization and study of the dynamical regimes that we introduce. Finally, in Section \ref{sec:Summary}, we summarize our results and draw conclusions.

\section{The structure of the crystal}
\label{sec:The structure of the crystal}
We consider photonic crystals created from two intersecting sets of dielectric sheets (see Fig. \ref{fig1}). One set is parallel to the $x$-$z$ plane and the other is parallel to the $y$-$z$ plane. The crystal is invariant, and taken to be infinite, along the $z$ axis. This creates a photonic crystal in which the dielectric sheets enclose rectangular air gaps, as shown in Fig. \ref{fig1}.

As in Refs. [\onlinecite{shep1,PhysRevA.46.612}], we characterize each dielectric sheet by the dielectric parameter $m=(\epsilon_{r}-1)d$, where $d$ and $\epsilon_{r}$ are, respectively, the width and relative permittivity of the sheet. At the lines where two sheets intersect, the relative permittivity is $2\epsilon_{r}-1$. At position $\mathbf{r}=(x, y)$ within the crystal, we take the local unit cell length in the $x$ and $y$ directions to be $l_{x}$ and $l_{y}$ respectively. In the limit $d$$\rightarrow$0, if the electric field vector of an electromagnetic wave of frequency $\omega$ is parallel to the $z$ axis, the local frequency versus wavevector dispersion relation, $\omega_{\mathrm{loc}}(\bm{\mu},l_{x},l_{y})$, of the wave satisfies the equations \cite{shep1},

\begin{subequations}
\begin{align}
\label{eqna}
\cos\left(\mu_{x}l_{x}\right)=\cos\left(k_{x}l_{x}\right)-\frac{m\omega_{\mathrm{loc}}^{2}}{2c^{2}k_{x}}\sin\left(k_{x}l_{x}\right)\\
\cos\left(\mu_{y}l_{y}\right)=\cos\left(k_{y}l_{y}\right)-\frac{m\omega_{\mathrm{loc}}^{2}}{2c^{2}k_{y}}\sin\left(k_{y}l_{y}\right),
\label{eqnb}
\end{align}
\end{subequations}
where $c$ is the speed of light in vacuo, $\bm{\mu}=$($\mu_{x}$,$\mu_{y}$) is the Bloch wavevector, and $\bm{k}$=($k_{x}$,$k_{y}$) is the local wavevector of the electromagnetic wave between the dielectric sheets. At time $t$, the local electric field magnitude, $E = E_{0}e^{i(\mathbf{k}.\mathbf{r}-\omega{t})}$, is determined by the wavevector $\mathbf{k}$. The Bloch wavevector, $\bm{\mu}$, determines the spatial development of the phase of the electromagnetic wave as it propagates through the crystal \cite{shep1}.

When the $y$-component of the wavevector between the dielectric sheets is evanescent, so that $k_{y} = iq_{y}$ where $q_{y}$ is real, Eq. (\ref{eqnb}) can be written in the form \cite{shep1}:

\begin{equation}	\cos\left({\mu}_{y}l_{y}\right)=\cosh\left({q}_{y}l_{y}\right)-\frac{m\omega_{\mathrm{loc}}^{2}}{2c^{2}{q}_{y}}\sinh\left({q}_{y}l_{y}\right).
\label{evenes}
\end{equation}

If the lattice parameters $m$, $l_{x}$ and $l_{y}$ vary sufficiently slowly, the local dispersion relation at any point in the crystal is, to good approximation, the same as the dispersion relation for an infinite crystal with a constant unit cell identical to the local unit cell \cite{crd}. Here, we choose $m$ and $l_{x}$ values that vary slowly with position and are defined by the continuous functions $l_{x} = l_{0}\exp(-\eta{x})$ and $m=m_{0}(1-\rho{y'}^{2})$, where the constants $l_{0}$, $m_{0}$, $\eta$, and $\rho$ are specified below. The $x' - y'$ axes, are related to the $x - y$ axes by a rotation of $\theta$ about the $z$ axis, as shown in Fig. \ref{fig1}.

The solutions of Eqs.(\ref{eqna}) and (\ref{evenes}) define a number of allowed frequency bands of the crystal. In the bands considered here, we show below that changes in the positions of both the top and bottom of the band, i.e. the highest and lowest frequencies, play a key role in driving the ray paths chaotic. For that reason, the lowest frequency band is of no interest here, because it always has a solution extending down to $\omega =0$, which means that chaotic ray paths within the band are unbounded on the right (i.e. for high $x$) \cite{crd}. Instead, the band of interest in this work is the next lowest frequency band in which the rays have a locally evanescent component in the $y$ direction and a locally propagating character in the $x$ direction \cite{crd,shep1}.

\section{The ray tracing}
\label{sec:The ray tracing}

The ray paths in the crystal are determined by the pair of Hamilton's equations \cite{crd,PhysRevE.70.036612}
\begin{subequations}
\begin{equation}
\frac{d\mathbf{r}}{dt}=\frac{\partial{H}}{\partial\bm{\mu}},\label{hamil1}
\end{equation}
\begin{equation}
{\frac{d\bm{\mu}}{dt}=-\frac{\partial{H}}{\partial\mathbf{r}}}.
	\label{hamil}
\end{equation}
\end{subequations}

\begin{figure}[t]
\centerline{

   \includegraphics[width =\linewidth]{fig2.pdf}
  }
	\caption{Dispersion surface, $\omega_{\mathrm{loc}}(\mu_{x},\mu_{y})$ calculated for $l_{x}=0.75$ $\mu$m, $l_{y}=0.5$ $\mu$m and $m_{0}=2$ $\mu$m. Three constant frequency contours are shown with $\omega = 5.7\times10^{14}$ rad s$^{-1}$ (dashed curve), $\omega = 6.75\times10^{14}$ rad s$^{-1}$ (solid curve) and $\omega = 7.35\times10^{14}$ rad s$^{-1}$ (dot-dashed curve). At the bottom of the figure the contours are shown projected onto the $\omega_{\mathrm{loc}}=0$ plane. Rays propagate perpendicular to these contours. One quadrant of the reduced Brillouin zone is shaded gray with its corners labelled A, B, C, D. The inset, top right, shows the repetition of the Brillouin zone and illustrates that the lowest and highest frequency contours (dashed and dot-dashed curves respectively) form closed curves while the intermediate contour (solid) forms an open curve.}
	\label{fig2}
\end{figure}

The 2D Hamiltonian is defined as \cite{crd}
\begin{equation}
	H(\mathbf{r},\bm{\mu},\omega)=\omega_{\mathrm{loc}}(\bm{\mu},l_{x},l_{y})-\omega,
	\label{disp}
\end{equation}where $\omega$ is the angular frequency of the electromagnetic wave and the local lattice constants $l_{x},l_{y}$ both depend on position \textbf{r}. To determine ray paths in the second band we first specify $\omega$ and the initial position of the ray front, both spatially in the crystal, ($x,y$), and the Bloch wavevector in the band, ($\mu_{x},\mu_{y}$). We then solve Eqs. (\ref{hamil1}) and (\ref{hamil}) numerically using a fourth-order Runge-Kutta method. It follows from Eqs.(\ref{hamil1}) and (\ref{disp}) that
\begin{equation}
	\frac{d\mathbf{r}}{dt}=\frac{\partial{\omega_{\mathrm{loc}}}}{\partial\bm{\mu}}.
	\label{pathexp}
\end{equation}

From Eq.(\ref{pathexp}) we see that the direction in which a ray propagates will always be perpendicular to the constant frequency contour $\omega = \omega_{\mathrm{loc}}$ on the dispersion surface.

Figure \ref{fig2} shows $\omega_\mathrm{loc}$ versus $\mu_{x}$ and $\mu_{y}$ at the point ($x,y$) = ($28.7$ $\mu$m, $y=11$ $\mu$m), in the crystal where $l_{x}=0.75$ $\mu$m, $l_{y}=0.5$ $\mu$m, and $m_{0}=2 $ $\mu$m. We also take $\theta = 21^{\circ}$ and $\eta$ = $10^{4}$ m$^{-1}$: parameters that will be used throughout this paper. The three constant frequency contours marked in
Fig. \ref{fig2} correspond to $\omega = 5.7\times10^{14}$ rad s$^{-1}$ (dashed curve), $\omega = 6.75\times10^{14}$ rad s$^{-1}$ (solid curve) and $\omega = 7.35\times10^{14}$ rad s$^{-1}$ (dot-dashed curve).

Due to the symmetry of the frequency band, we need only consider one quadrant of the reduced Brillouin zone (gray shaded region in Fig. \ref{fig2}) for which $0\leq\mu_{x}\leq\pi/l_{x}$ and $0\leq\mu_{y}\leq\pi/l_{y}$. In fact, it is the four corners (marked A, B, C and D in Fig. \ref{fig2}) of this reduced Brillouin zone quadrant i.e. the points where $\mu_{x}=0$ or $\pi/l_{x}$ and $\mu_{y}=0$ or $\pi/l_{y}$ that will be of most interest here.

The inset in Fig. \ref{fig2} reveals that, since the Brillouin zone repeats with a period of $2\pi/l_{x}$ in the $\mu_{x}$ direction and $2\pi/l_{y}$ in the $\mu_{y}$ direction, the lowest frequency contour at $\omega = 6.75\times10^{14}$ rad s$^{-1}$ (dashed curve), and the highest frequency contour at $\omega = 7.35\times10^{14}$ rad s$^{-1}$ (dot-dashed curve), both form closed curves. However, this is not the case for the intermediate contour at $\omega = 6.75\times10^{14}$ rad s$^{-1}$ (solid curve), which is open in the extended zone scheme.

Since the frequency band varies monotonically in both the $\mu_x$ and $\mu_y$ directions over the shaded section of the reduced Brillouin zone in Fig. \ref{fig2}, the gradient $\partial\omega_\mathrm{loc}/\partial\bm{\mu}$ is only parallel to the $\mu_{x}$ axis along the lines $\mu_{y}=0$ or $\pi/l_{y}$, and only parallel with the $\mu_{y}$ axis along the lines $\mu_{x}=0$ or $\pi/l_{x}$. When contours form open curves they are restricted to lie either between $\mu_{y}=0$ and $\pi/l_{y}$, or between $\mu_{x}=0$ and $\pi/l_{x}$. Since a ray propagates perpendicular to the constant frequency contour where $\omega_\mathrm{loc} = \omega$, if this contour forms an open curve there are directions in which the ray cannot propagate. For example, it can be seen from Fig. \ref{fig2} that for the (solid) constant frequency contour at $\omega = 6.75\times10^{14}$ rad s$^{-1}$, rays cannot propagate parallel, or almost parallel, to the $y$ axis, because $\omega_\mathrm{loc}$ is never parallel to the $\mu_{x}$ axis. Below, we show that this restriction causes spatial localization of the rays in the $y$ direction.

For a given $\omega$, a constant frequency contour forms a closed loop if $\omega = \omega_\mathrm{loc}$ is between the bottom of the band, point A in Fig. \ref{fig2}, and the saddle point B. The contour is also closed if $\omega_\mathrm{loc}$ is between the top of the band, point D in Fig. \ref{fig2}, and the saddle point C. The constant frequency contours between the two frequencies corresponding to $\omega_\mathrm{loc}$ at points B and C always forms open curves.

\section{The shape of the ray paths}
\label{sec:The shape of the ray paths}
Henceforth, we consider crystal parameters, $l_{y}= 1$ $\mu$m, $l_{0} =1$ $\mu$m, $\theta = 21^{\circ}$, $\eta=1\times10^{4}$ m$^{-1}$, $m_{0}=2$ $\mu$m, $\rho =1\times10^{10}$ m and, unless otherwise stated, take $\omega =$ $6\times10^{14}$ rad s$^{-1}$. When there is an evanescent component to the electric field, this is in the $y$ direction.

Spatial variation of the unit cell changes both the shape of the dispersion curve, $\omega_{\mathrm{loc}}(\bm{\mu},l_{x},l_{y})$, and the range of frequencies that it spans. Thus, in parts of the crystal the electromagnetic wave may lie within an allowed band,  but in other parts its frequency coincides with a bandgap.

It is therefore essential to identify where in the crystal $\omega$ coincides with an extremum (points A and D in Fig. \ref{fig2}) or a saddle point (points B and C in Fig. \ref{fig2}) in the dispersion surface.

\begin{figure}[t]
\centerline{

   \includegraphics[width =\linewidth]{fig3.pdf}
  }
	\caption{Loci of points in the crystal where $\omega=$ $6\times10^{14}$ rad s$^{-1}$ coincides with the $\omega_{\mathrm{loc}}$ values at points A (solid curve), B (dotted curve), C (dot-dash curve) and D (dashed curve) in the reduced Brillouin zone shown in Fig. \ref{fig2}. In the gray regions, $\omega$ lies in a bandgap, and hence there are no propagating solutions. Rays can only propagate in the white regions bounded by the solid and dashed curves where $\omega$ coincides with the band minimum and maximum, respectively, shown in Fig. \ref{fig2}. Within the black regions, $m$ is negative, meaning that either $\epsilon_{r}$ or $d$ must also be negative. Rays cannot reach these regions of negative permittivity because they are unable to traverse the outer gray area where $\omega$ lies within a bandgap. Consequently, the regions of negative permittivity do not affect the ray dynamics that we consider.}
	\label{fig3}
\end{figure}

To illustrate this, Fig. \ref{fig3} shows the four loci of points in the crystal at which $\omega$ coincides with the two extrema or the two saddle points in the local $\omega_{\mathrm{loc}}(\bm{\mu},l_{x},l_{y})$ surface (i.e. points A-D in Fig. \ref{fig2}). The solid, dotted, dot-dashed and dashed curves correspond to points A, B, C and D respectively. Between curves A and D, the white region in Fig. \ref{fig3}, $\omega$ lies within the second allowed frequency band. Whilst it is not universally true that point B lies at a lower frequency than point C, as can be seen from the crossing of curves B and C at $x = x_{cross} \approx -48$ $\mu$m in Fig. \ref{fig3}, this is the case throughout the region of interest here. The gray region in Fig. \ref{fig3} shows the regions of the crystal for which there are no propagating solutions at frequency $\omega$. In the black region, $m<0$, meaning that either $\epsilon_{r}$ or $d$ would need to be negative. Although some materials do have negative values of permittivity, we do not consider them here.

As discussed above, at any point in the crystal a ray can, in principle, propagate in any spatial direction provided that the $\omega_{\mathrm{loc}} = \omega$ contour forms a closed loop. By contrast, the range of possible propagation directions is limited for open contours. In Fig. \ref{fig3}, when $x > x_{cross}$, at any point in the crystal that lies between curves A and B, or between curves C and D, the iso-frequency contour for $\omega_\mathrm{loc} = \omega =$ $6\times10^{14}$ rad s$^{-1}$ forms a closed loop. Conversely, for any point in the crystal between curves B and C, the iso-frequency contour forms an open curve, which restricts the range of directions in which a ray may propagate.
\begin{figure}[t]
\centerline{

   \includegraphics[width =0.9\linewidth]{fig4.pdf
  }
	\caption{Ray paths calculated in a region of the crystal where all trajectories are stable. The four curves are the loci of points in the crystal where $\omega=$ $6\times10^{14}$ rad s$^{-1}$ coincides with the $\omega_{\mathrm{loc}}$ values at points A (solid curve), B (dotted curve), C (dot-dash curve) and D (dashed curve) in the reduced Brillouin zone. These four curves strongly influence the shape of the ray paths and determine the turning points.}
	\label{fig4}
\end{figure}

\begin{figure}[t]
\centerline{

  \includegraphics[width =\linewidth]{fig5.pdf}
  }
\caption{(a) Two chaotic ray paths propagating in two distinct regions of the photonic crystal when $\omega = $ $6.09\times10^{14}$ rad s$^{-1}$. The crystal parameters are $l_{y}= 1$ $\mu$m, $l_{0} =1$ $\mu$m, $\theta = 21^{\circ}$, $\eta=1\times10^{4}$ m$^{-1}$, $m_{0}=2$ $\mu$m, $\rho =1\times10^{10}$ m. Panels (b) and (c) are enlargements of the left and right-hand boxes in (a). Crosses in (b) and (c) mark the points where Bragg reflections occur.}
	\label{fig5}
\end{figure}

Figure \ref{fig4} shows a selection of stable ray paths in the crystal. The turning points of these rays are produced either by Bragg reflection, whenever $\mu_{x}$ = $\pm\pi/l_{x}$ or $\mu_{y}$ = $\pm\pi/l_{y}$, or by the rays reaching band extrema away from the Brillouin zone boundaries as a result of the band changing shape throughout the crystal. Figure \ref{fig4} reveals that the ray paths are shaped by the shifting of the bandstructure, with curves A, B, C and D passing through extrema in the envelopes of the ray trajectories. Between curves A and B, Bragg reflections occur when $\mu_{x}=\pm\pi/l_{x}$. At frequencies above that at point B in Fig. \ref{fig2}, such reflections no longer occur because the iso-frequency contours in Fig. \ref{fig2} only intersect with the edge of the Brillouin zone where $\mu_{y}=\pm\pi/l_{y}$ (between points B and D).

\section{Dynamical Barriers}
\label{sec:Dynamical Barriers}
Previous work has shown that the phase space of rays in the photonic crystal contains mixed stable-chaotic regions and that, for certain $\omega$, two or more chaotic regions are separated by islands of stability \cite{crd}. A trajectory starting in one chaotic sea cannot cross the stable island and is therefore unable to enter the second chaotic sea. Consequently, the stable island is known as a dynamical barrier. Although there is sometimes diffusion across dynamical barriers, such as via cantori (see, for example, [\onlinecite{TTC}]), in the photonic crystals considered here, the dynamical barrier can be completely impenetrable, localizing chaotic rays to two distinct regions of the phase space.

In this section, we explain the existence of these dynamical barriers and explore their effect on ray transport. The dynamical barriers occur for a wide range of $\omega$ and, at the higher frequencies, separate the chaotic regions in real space as well as in phase space. Consequently, dynamical barriers provide a mechanism for controlling the transmission of light through photonic crystals.

Figure \ref{fig5}(a) shows two distinct chaotic paths in the photonic crystal that are almost separated in real space.  Figures \ref{fig5}(b) and (c) show enlargements of the regions within the boxes in (a), in which the rays are driven chaotic. The solid curve, (A), in Fig. \ref{fig5} marks the loci of points where the bottom of the frequency band (point A in Fig. \ref{fig2}) is at $\omega_\mathrm{loc}=$ $6.09\times10^{14}$ rad s$^{-1}$, whilst the dashed curve, (D), marks the loci of points where the \emph{top} of the band (point D in Fig. \ref{fig2}) is at $\omega_{\mathrm{loc}}=$ $6.09\times10^{14}$ rad s$^{-1}$.

The crosses in Fig. \ref{fig5} (b,c) mark the points along the real-space ray trajectory where the Bloch wavevector, $\bm{\mu}$, is at an edge of the reduced Brillouin zone shown in Fig. \ref{fig2}. At such points, the electromagnetic wave Bragg reflects along either the $x$ or $y$ direction, corresponding to a turning point of the classical ray. Most of these turning points occur away from the frequency band extrema labelled A, B and D in Fig. \ref{fig2} and therefore also away from the edges of the classically-allowed (white) region in Fig. \ref{fig5} (b,c). But, occasionally, Bragg reflection occurs at, or very near to, one of these extrema. For example, the crosses situated exactly on the dashed curve in Fig. \ref{fig5} (b), which is the locus of points in real space along which the electromagnetic wave frequency $\omega$ coincides with the top of the frequency band at Point D in Fig. \ref{fig2}, correspond to Bragg reflections along the $y$ direction occurring at Point D.

\begin{figure}[t]
\centerline{

   \includegraphics[width =0.95\linewidth]{fig6.pdf}
  }
	\caption{A Poincar\'e section in which a point is plotted each time a ray turns from traveling along the negative to the positive $x$-direction. The points are generated by three ray paths: the two chaotic trajectories shown in Fig. \ref{fig5} and a stable ray path that separates them. Points produced by the upper path in Fig. \ref{fig5} are marked with crosses, while those produced by the lower path are marked with circles. Points generated by a stable path in the dynamical barrier are marked with triangles.}
	\label{fig6}
\end{figure}

\begin{figure*}[t]
\centerline{

   \includegraphics[width =\linewidth]{fig7.pdf}
  }
	\caption{Dispersion surfaces $\omega_\mathrm{loc}(\mu_{x},\mu_{y})$ calculated at three different positions in the photonic crystal: (a) $x=0$ $\mu$m, $y'=0$ $\mu$m where $l_{x} = l_{y} = 1$ $\mu$m and $m=2$ $\mu$m; (b) $x=50$ $\mu$m, $y'=0$ $\mu$m where $l_{x} = 0.607$ $l_{0}$ $\mu$m, $l_{y} = 1$ $\mu$m and $m=2$ $\mu$m; (c) $x=0$ $\mu$m, $y'=7.07$ $\mu$m where $l_{x} = l_{y} = 1$ $\mu$m and $m=1$ $\mu$m. The iso-frequency contours, shown both on the dispersion surface and projected onto the $\omega_\mathrm{loc}=0$ plane beneath, are equally spaced by $3\times10^{13}$ rad s$^{-1}$. As $l_{x}$ decreases, the band shifts to higher $\omega_\mathrm{loc}$, as can be seen by comparing the dispersion surface in (b) with that in (a). In addition, over large sections of the dispersion surface in (b), the iso-frequency countours are almost parallel to the $\mu_{y}$ axis, meaning that rays are, in general, restricted to propagate in directions close to the $x$ axis. Comparing (c) to (a) reveals that as $m$ decreases, the band shifts to higher $\omega_\mathrm{loc}$ and also broadens.}
	\label{fig7}
\end{figure*}

\begin{figure}[b]
\centerline{

   \includegraphics[width =0.7\linewidth]{fig8.pdf}
  }
	\caption{A selection of rays in the crystal with $\omega$ = (a) $6.15\times10^{14}$ rad s$^{-1}$, (b) $6.87\times10^{14}$ rad s$^{-1}$. Also shown are the loci of points in the crystal where $\omega = \omega_{\mathrm{loc}}$ at points A (solid curve), B (dotted curve), C (dot-dash curve) and D (dashed curve) in the reduced Brillouin zone shown in  Fig. \ref{fig2}. In the gray regions there are no propagating solutions at the given $\omega$.}
	\label{fig8}
\end{figure}

The dashed curve in Fig. \ref{fig5} (a,b) is also the boundary between regions where waves can (white) and cannot (gray) propagate. Note that for $y \lesssim -2$ $\mu$m, this separates the allowed region into two segments that occupy distinct ranges of $x$ values. As noted above, when rays approach the dashed curve in Fig. \ref{fig5} they Bragg reflect. Since this boundary is so strongly curved, it makes the ray path highly sensitive to the initial conditions, thereby driving paths that reflect from it chaotic.

These ray trajectories have some similarities with the classical orbits of particles in a Sinai billiard comprising a rectangular outer wall, which encloses a circular scattering barrier. Particles within the billiard move between these two impenetrable walls. Orbits that interact with the circular barrier are chaotic because reflections from that barrier couple the motion parallel and perpendicular to the outer wall. Similarly, in the photonic crystal considered here, chaotic ray orbits are generated by reflections near the dashed boundary labelled D in Fig. \ref{fig5}.

By contrast, the trajectory of the right-hand path in Fig. \ref{fig5} (a) and enlarged in part (c), is driven chaotic by reflection from the concave (right-hand) end of the white (classically-allowed) region. In Bunimovich stadia, comprising straight parallel edges with semicircular walls at either end, chaos occurs due to reflections from the curved ends, which mix motion parallel and perpendicular to the side walls. In a similar way, ray paths confined near the concave right-hand end of the white allowed region in Fig. \ref{fig5} are also driven chaotic.

Rays that do not encounter either the concave end of curve A or the convex region around barrier D remain stable, and hence form a dynamical barrier that separates the two chaotic paths in Fig. \ref{fig5}.

Figure \ref{fig6} is a Poincar\'e section in which a point is plotted each time a ray turns from traveling in the negative $x$-direction to the positive $x$-direction. Points corresponding to three different ray paths are shown. The crosses are generated by the upper of the two ray paths in Fig. \ref{fig5} (a), whilst the circles correspond to the lower ray path. The broad spread of these two sets of points in the Poincar\'e section confirms that each ray is chaotic. The triangular points in Fig. \ref{fig6} are generated by a stable ray path (not shown) forming the dynamical barrier that separates the two chaotic orbits in Fig. \ref{fig5}(a). Since this ray is stable, it generates points on a smooth continuous curve in the Poincar\'e section.

To fully understand the origin of the dynamical barrier, it is useful to consider in more detail the bandstructure changes, throughout the crystal, produced by the variation of $l_{x}$ in the $x$ direction, and $m$ with $y'$.

Figure \ref{fig7} shows dispersion surfaces, $\omega_\mathrm{loc}(\mu_{x},\mu_{y})$, and iso-frequency contours at, (a-c), three different spatial points in the crystal. It illustrates how variations in $l_{x}$ and $m$ both change the bandstructure. The effect of changing $l_{x}$ can be seen by comparing Figs. \ref{fig7}(a) and (b). In (a) $x=0$ $\mu$m, where $l_{x} = l_{0}$, and in (b) $x=50$ $\mu$m, where $l_{x} =$ 0.607 $l_{0}$. In both cases, $y'=0$, and $m=2$  $\mu$m. Reducing $l_{x}$, i.e. moving from (a) to (b), shifts the band to a higher range of frequencies. In addition, reducing $l_{x}$ makes $\omega_\mathrm{loc}$ far less sensitive to changes in $\mu_{y}$, as revealed by comparing Fig. \ref{fig7}(b) with Fig. \ref{fig7}(a).

This reduced variation of $\omega_\mathrm{loc}$ with $\mu_{y}$ means that far more iso-frequency contours form open curves in Fig. \ref{fig7}(b) than in Fig. \ref{fig7}(a), and that the curvature of these contours decreases. The reduction of the curvature of the contours restricts the range of spatial directions in which a ray may propagate. For example, in Fig. \ref{fig7}(b), most rays propagate in directions almost parallel to the $x$ axis.

The effect of changing $m$ on $\omega_\mathrm{loc}(\mu_{x},\mu_{y})$ may be seen by comparing Figs. \ref{fig7}(a) and (c), for which $m=2$ $\mu$m and $m=1$ $\mu$m respectively with fixed $l_{x} = 1$ $\mu$m. As $m$ decreases, the band shifts to higher values of $\omega_\mathrm{loc}$ and broadens so increasing the range of frequencies for which closed contours are found about points A and D.

We now use these changes in the bandstructure to explain more fully the ray dynamics. Figure \ref{fig8} shows rays in the crystal calculated for  $\omega =$ (a) $6.15\times10^{14}$ rad s$^{-1}$ and (b) $6.87\times10^{14}$ rad s$^{-1}$. The solid, dotted, dot-dashed and dashed curves show, respectively, the loci where $\omega_{\mathrm{loc}}$ coincides with points A, B, C, and D in the Brillouin zone (Figs. \ref{fig2} and \ref{fig7}).

The first point to note is that the (white) region in Fig. \ref{fig8}(b) in which the rays may propagate is located at higher $x$ values than in Fig. \ref{fig8}(a). This is because the band spans higher frequencies when $l_{x}$ is smaller (see Fig. \ref{fig7}), i.e. when $x$ is larger, and so at higher $\omega$ the rays propagate further along the $x$ axis.

Comparing Fig. \ref{fig8}(a) and (b) reveals that at higher $\omega$ [Fig. \ref{fig8}(b)] each ray is more confined in the $y$-direction. This is a consequence of the rays propagating at angles that are closer to the $x$ axis at higher $\omega$; an the effect that can be understood by comparing Figs. \ref{fig7}(a) and (b). Hence, the higher the value of $\omega$, the greater the restriction on the propagation angles, and the narrower the ray path along the $y$ direction. At higher $\omega$, the regions of the crystal in which rays can travel in any direction, i.e. the regions between curves A and B, and curves C and D, are reduced. This corresponds to the reduced variation of $\omega_\mathrm{loc}$ with $\mu_{y}$ at higher $\omega$, as shown in Fig. \ref{fig7}(b).

If $\omega$ is sufficiently low, for this structure when $\omega \lesssim 5.91\times10^{14}$ rad s$^{-1}$, rays in the crystal encounter both of the regions (i.e the concave and convex barriers in Fig. \ref{fig5}) that generate chaos. At higher $\omega$, the spread of each ray orbit in the $y$ direction is reduced, and a ray that encounters one of the regions where it is driven chaotic does not reach the other. When $\omega \gtrsim 6.12\times10^{14}$ rad s$^{-1}$, a region forms in the crystal where rays will encounter neither of the strongly curved barriers. These rays are stable and collectively form the dynamical barrier.

As $\omega$ rises above $\approx 6.6\times10^{14}$ rad s$^{-1}$, the two distinct regions of the crystal that induce chaotic ray paths shrink, and become increasingly localized near the concave and convex barriers. This increases the separation of the two sets of chaotic orbits in real space. If $\omega$ is increased further, the right-hand chaotic region disappears completely, as shown in Fig. \ref{fig8}(b), meaning that the dynamical barrier also vanishes. An examination of rays near the right-hand concave barrier [within the right-hand box in Fig. \ref{fig5}(a)] reveals that, due to the shifting bandstructure throughout the crystal and the effective force that this exerts on the rays, such rays are more complex than those in Bunimovich stadia. Consequently, the exact reason for the suppression of chaos in this region, which occurs at high $\omega$, is not yet fully understood. However, as the ray paths become increasingly restricted to a small region around the center of the concave barrier, chaos disappears because the barrier acts on the orbits as though it is locally flat. By contrast, the chaotic orbits created by the left-hand convex barrier in Fig. \ref{fig5} persist for even higher $\omega$.

\section{Proposed experimental realization of the modulated photonic crystal and associated ray dynamics}
\label{sec:experiment}

Microwave analogues offer major advantages for investigating the propagation of electromagnetic waves through dielectric media and the relation between the waves and underlying ray dynamics \cite{Stoeckmann}. Due to their large scale, photonic crystals for microwaves can be made very accurately with imperfections far smaller than the wavelength of the microwaves. Such imperfections therefore have a negligible effect on the wave transmission processes. For example, modern computer-controlled milling machines can produce holes in a Teflon dielectric block with a precision of $\pm 0.05$ mm: orders of magnitude smaller than the wavelength of microwaves. In addition, the electric field profile of the electromagnetic modes can be directly measured in microwave systems \cite{Stoeckmann}, thus enabling study of, for example, the link between modal form and the transmission coefficient of the system.

Recent experiments on the transmission of microwaves through 1D photonic crystals comprising Teflon sheets have revealed that absorption of the microwaves by the Teflon has little effect on the shape of the measured transmission spectrum, which is in excellent quantitative agreement with the corresponding calculations \cite{StockNJP}. Since absorption does not destroy coherent wave phenomena, in particular band formation, we expect that it will have a similarly small effect on the band transport processes discussed above. Consequently, modulated microwave photonic crystals fabricated by milling cm-scale air holes into a Teflon sheet, or high-refractive-index (3.3) ceramic-filled plastic \cite{ceramic}, offer a promising starting point for the experimental verification and study of the dynamical effects discussed above, and their effect on electromagnetic wave transmission. We note that photonic crystals with a gradient index have been successfully realized experimentally for metamaterials \cite{Mei_2009,Chen_2009,Liu_2009,Cai_2007,Schurig_2006,Smith_2005}, and such systems might also be suitable for experimental studies of band transport phenomena in modulated photonic crystals.

Here, though, we focus on possible microwave realizations of the modulated photonic crystals. To ensure maximal correspondence with the system shown in Fig. \ref{fig5}, and analyzed in detail above, the microwave photonic crystal would have rectangular air holes separated by thin dielectric walls. The spatial variation of the hole and wall widths follows from the requirement that $l_{x} = l_{0}\exp(-\eta{x})$ and $m=(\epsilon_{r}-1)d=m_{0}(1-\rho{y'}^{2})$, as discussed in Section \ref{sec:The structure of the crystal}. Providing the walls are much narrower than the air holes, the local dispersion relation of the frequency bands will be accurately described by Shepherd's analytical model \cite{shep1} (see Section \ref{sec:The structure of the crystal}). We note, however, that exact dispersion relations can be determined for any unit cell geometry by using standard techniques such as expansion over plane waves.

As in previous experiments \cite{Stoeckmann,Stein_1995}, quasi 2D microwave photonic crystals could be used because the width of the system along $z$ does not significantly affect either the frequency band structure or the resulting ray dynamics. In such structures, the dielectric block is $\approx 1$ cm thick along the $z$ direction and enclosed by copper plates, which form a microwave cavity. To study transport through the 2D photonic crystal, continuous microwaves would be injected through a wire antenna, of diameter $\approx$ 0.1 mm, which passes through the top plate at a fixed position, $\bm{r}$. A vector network analyzer would be used to measure the spectrum $T(\omega, \bm{r}, \bm{r'})$ for transmission to a receiving wire antenna at a variable position $\bm{r'}$ in the bottom plate for $\omega$ in the range $30 \times 10^{12} \lesssim \omega \lesssim 250 \times 10^{12}$ rad s$^{-1}$ \cite{Stoeckmann,Stein_1995}.

A key advantage of using a vector network analyzer is that for each $\omega$ value, the electric field profile, $E(x, y)$, can be mapped experimentally by using a moveable bottom plate to scan the receiving wire across the structure and analyzing how $T(\omega, \bm{r}, \bm{r'})$ changes with $\bm{r'}$ \cite{Stoeckmann}. Since both the modulus and sign of $E(x, y)$ can be determined, continuous waves can study pulse propagation via a simple Fourier transform of $T(\omega, \bm{r}, \bm{r'})$ to the time domain \cite{Stein_1995}. This Fourier technique, which is simpler than generating microwave pulses \cite{Stoeckmann}, could be used to investigate the effects of dynamical barriers on pulse propagation by measuring how $T(\omega, \bm{r}, \bm{r'})$ varies with the positions of the two antennae, with $\omega$, and with $\theta$.

For $\theta$ values that generate a dynamical barrier, which separates chaotic trajectories into distinct regions of phase space (Figs. \ref{fig5} and \ref{fig6}), the dynamical barrier will reduce the range of ray trajectories that directly link the two antennae, thereby producing a measurable decrease in transmission between them. As shown in Fig. \ref{fig8}, the location, and even the existence, of the dynamical barrier varies rapidly with $\omega$. Consequently, we expect that $T(\omega, \bm{r}, \bm{r'})$ will also demonstrate high sensitivity to changes in $\omega$. Providing the parameters of the photonic crystal are accurately known, we expect good quantitative agreement between experiment and theory, which will help to elucidate the effect of the dynamical barriers on ray and wave transmission.

The aim of the proposed microwave experiments is to investigate the feasibility of using dynamical barriers to control electromagnetic wave propagation through spatially-modulated photonic crystals and so provide proof-of-principle demonstration of this concept. We emphasize that dynamical barriers occur in many systems with a mixed stable-chaotic classical phase. In the electromagnetic system that we consider here, their existence requires spatial modulation of the bandstructure, which couples motion in the $x$ and $y$ directions, but does not depend on the precise details of the lattice structure used to produce that modulation: for example the shape of the unit cell. Consequently, the dynamics that we consider have the potential for scaling to optical wavelengths, where the air holes are usually circular rather than rectangular. A rectangular unit cell speeds up the ray calculations, making it easier to explore the large parameter space available, but is not essential to generate dynamical barriers, which should occur in a range of modulated photonic crystal structures.

\section{Summary}
\label{sec:Summary}

We have shown that spatial modulation of the lattice parameters and, hence, the local bandstructure of a photonic crystal affects the stability, form, and location of Hamiltonian ray paths within it. The formation of convex or concave barriers at the edges of the classically-allowed region drives orbits that interact with those barriers chaotic. As $\omega$ increases, changes in the dispersion relation for the second allowed band make the ray paths increasingly localized in the $y$ direction. In turn, this confines the chaotic ray trajectories to smaller areas around the convex and concave barriers at the edges of the classically-allowed region. The location and extent of the chaotic trajectories depend strongly on the value of $\omega$. For certain $\omega$, only a single region of chaos exists. However, as $\omega$ increases, this splits into two distinct regions of chaotic ray paths, located near either the convex or the concave barrier. These chaotic regions are separated by a dynamical barrier comprising stable ray orbits. When $\omega$ is just large enough for the dynamical barrier to form, this barrier is leaky because, in some regions of the crystal, chaotic orbits that are isolated in real space overlap in phase space. But as $\omega$ increases, the chaotic regions separate fully in both real and phase space. In this regime, the chaotic orbits cannot penetrate the dynamical barrier and are thus unable to propagate through the crystal. As $\omega$ increases further, the chaotic rays become so localized that those near the concave barrier disappear completely, thus removing the dynamical barrier.

We conclude that rays in slowly-modulated photonic crystals exhibit unique and rich dynamics, which are highly sensitive to both the spatial structure of the crystal and the value of $\omega$. Dynamical barriers formed by the stable rays provide a mechanism for controlling light transmission in certain frequency ranges. The exponential separation rate of two chaotic rays with slightly different initial conditions also strongly affects the propagation of the electromagnetic radiation. This mechanism could be exploited in optical switches or routers and may also enhance angular dispersion due to the superprism effect in photonic crystal structures \cite{x1}, which has potential for applications in wavelength division multiplexing devices. We hope that our results will stimulate the further work required to determine how \emph{ray} chaos affects the transmission of electromagnetic \emph{waves} through modulated photonic crystals, and to test the validity of Hamiltonian optics in this complex regime of nonlinear dynamics.

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Q: WCF vs Sync Framework We have an application that we developed using ASP.Net and the database is SQL SERVER 2008 R2. Now we are planning to decentralize this application. Then there will be one central database and several client databases. We have to synchronize all of these databases.
For example, in the morning all the updated master data have to be updated in the clients sites and in the night all the transactional data have to be updated on the central data bases.
What is the best way to achieve this using Microsoft technologies? So far I have thought of WCF service or the MS Synchronization framework.
Which is best?
What are limitations?

A: I would recommend the Sync framework for your scenario.  WCF is feasible but would require a fair bit of coding depending on how much data you are talking about.
A major consideration with the Sync framework is whether your SQLServers are on the same network or not.  If they are not on the same network, the app that performs the sync needs to be able to connect to the remote SQLServer.  If the remote SQLServer is behind a firewall, you will need to open a port which can be problematic (some security pros don't like having a SQLServer exposed publicly, even if it is over a port).
The other thing with the sync framework is that you have to have a timestamp column ( or equivalent I think from memory) on every table that you want to sync.  The framework will create a tracking table for every table you wish to sync.

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3 Tips to Tackle Decision Paralysis
AI Finds Drug Candidate for Liver Cancer in 30 Days
Rediscovering Hope Amidst Chaos
Moses Ma
The Tao of Innovation
The Power of Humor in Ideation and Creativity
Research shows that humor can help people be more creative in problem solving.
Source: Moses Ma/DepositPhoto
The hallmark of a really effective brainstorming is an abundance of genuine and heartfelt laughter. There's a reason for this: Laughter can help people solve problems that demand creative solutions, by making it easier to think more broadly and associate ideas/relationships more freely.[1] Recent research shows that people in a lighter mood experience more eureka! moments and greater inspiration.
Karuna Subramaniam, in research she did when she was with Northwestern University, found that boosting the mood of volunteers increased their likelihood of having an aha! moment as measured by their ability to solve a word association puzzle, the standard test for creative problem solving. Those who watched a comedy were measurably better at the task using insight than those who watched a horror film, or worse yet, a lecture about quantum electronics.
Using functional MRI, Subramaniam discovered that creative insight is correlated with increased activity in the brain's anterior cingulate cortex (ACC) just prior to solving a problem. This region is involved in regulating attention and in problem solving. And people in a positive mood generally have more ACC activity going into the task, which probably helped prepare the brain to find novel solutions. Participants who watched scary movies, such as The Shining, which was specifically noted in the research as "anxiety-producing," resulted in less activity in the ACC and demonstrated less creativity in solving the puzzles.
In fact, in another brainstorming study [2], where 84 participants—students, professional designers and improvisational comedians—took a cartoon caption humor test and a nominal product brainstorming test, the improvisational comedians generated 20 percent more ideas than professional product designers did, and the comedians generated ideas that were also rated 25 percent more creative. The study also found that many of the games used in improvisational comedy training could be effectively adapted to product design idea generation, because they strongly promoted associative thinking—and found that it increased idea output on average by 37 percent in a subsequent product brainstorming session.
Also, Rex Jung, an assistant research professor of neurosurgery at the University of New Mexico and a practicing clinical neuropsychologist proposes that creative capacities are not the same as intellectual capacities. The ability to acquire and process facts and observations—to reason—is fundamentally different from the ability to put them together in innovative ways. When we perform intellectual tasks, neural networks appear to function in more directed and linear ways. However, when we attempt to perform more creative tasks, it is as if the neural pathways plot more meandering and circumlocutory paths. Jung calls this alternative brain functioning transient hypofrontality, which suggests that our usual neural process of seeing and processing the world switches off for a while to make space for a different kind of engagement.
What this means for the innovation manager and brainstorm facilitator is that humor, lightened mood, and mental spaciousness are important when it comes to encouraging creativity, ideation, and problem solving. Jung explains, "Creative people usually know what activities precipitate their best ideas. It can be anything from going for a run to meditation." Also, it validates that all those crazy warm-up exercises that innovation consultants make you do have a scientific basis—and that it is indeed possible to teach creativity.
The Neurophysiology of Laughter
In fact, there's an entire branch of science that studies the psychological and physiological effects of humor and laughter on the brain and the immune system— it's called gelotology and studies in this area are proliferating. Researchers have found that humor and laughter is a very complex cognitive function.
For example, EEG topographical brain mapping has shown that the entire brain has to work together to appreciate a joke fully and for humor to work. First, the left hemisphere begins to process the words, then the frontal lobe center of emotionality is activated, 120 milliseconds later the right hemisphere begins processing the pattern and a few milliseconds later the occipital lobe shows increased activity. Delta waves are increased as the brain "gets" the joke, and the nucleus accumbens to elicit happiness felt as a reward, and finally, laughter erupts. [3] But essentially, the left hemisphere sets up the joke, and the right hemisphere helps the brain "get" the joke. Damage to the right frontal lobe of the cerebrum can decrease one's ability to appreciate humor, smile, or laugh in response to a joke.
This is quite different from what happens with your typical emotional responses. Emotional responses appear to be confined to specific areas of the brain, while laughter seems to be produced via a circuit that runs through many regions of the brain. These connections are involved in the control of major activities like friendship, love and affection, and it makes sense that the involuntary action of laughter forms a direct communication link between people, from limbic brain to limbic brain. People who relish each other's company laugh easily and often; those who distrust or dislike each other laugh little, if at all. Thus laughter promotes bonding and team-building.
Researchers are also finding that there are many other benefits to laughter and humor. For example, it stimulates both sides of the brain to enhance learning, by activating the limbic system in the brain and connecting the right and left sides. Also, humor releases tension, which can lead to perceptual flexibility—a required component of creativity.
Evolutionary Roots of Humor
So why did humans develop a sense of humor in the first place? If you look at a typical brainstorming as an ethnographer, you can see the roots of group thinking as a survival mechanism for tribal collectives. If game became sparse, the best hunters and shamans would gather, to discuss strategies for survival. What we see in corporate boardrooms and brainstormings has this as a lineage. Thus, the underlying behaviors can be deconstructed by using an approach based on evolutionary psychology to analyse technical and practices in brainstorming.
Robert Provine, a professor of neurobiology and p sychology at the University of Maryland has made a serious study of laughter, in the same way that an animal behaviorist might study a dog's bark or a bird's song. He believes that laughter, like the bird's song, functions as a kind of social signal. Other studies have confirmed that theory, showing that people are 30 times more likely to laugh in social settings than when they are alone.
Cultural anthropologist Mahadev Apte says, "Laughter occurs when people are comfortable with one another, when they feel open and free. And the more laughter there is, the more bonding occurs within the group." This feedback loop of bonding-laughter-more bonding may be a reason why laughter is contagious. Philosopher John Morreall believes that the first human laughter may have begun as a gesture of shared relief at the passing of danger. And since the relaxation that results from a bout of laughter inhibits the biological fight-or-flight response, laughter may indicate trust in one's companions. Also, studies have also found that dominant individuals, such as the boss or the tribal chief, generally use humor more than their subordinates. In such cases, Morreall explains, controlling the laughter of a group becomes a way of exercising power by controlling the emotional climate of the group.
In fact, in a study by the McClelland Centre for Research and Innovation, it was found that outstanding executives use humor more than twice as often as the so-called average executives (237 percent more, to be exact). Furthermore, when the study examined executives' compensation, there was a direct correlation between the use of humor and the size of their compensation. The funnier they were, the more they made. This is why Steve Jobs' keynote speech launching the iPhone clocked in at .6 laughs per minute—not good enough for the Tonight Show, but better than most new comics. For the innovation manager and brainstorm facilitator, humor and laughter are effective tools for strengthening human connection and controlling group behavior.
Understanding the Cognitive Structure of Jokes
If we seek to utilize humor as part of a formal approach to group ideation, it makes sense to better understand the structure of humor. Currently, there are three theories of humor—superiority theory, comic relief theory, and incongruity theory. Let's examine each of these approaches and theories of humor.
Superiority humor deals with jokes that focus on someone else's mistakes, stupidity, or misfortune, as in the typical jokes about blondes or ethnicities. This could also include self-deprecation, which is often used by stand-up comedians and in Woody Allen movies.
Here's an innovation-related joke that uses this form of humor.
One night, a Delta twin-engine puddle jumper was flying somewhere above New Jersey. There were five people on board: the pilot, a venture capitalist, the Dalai Lama, and a hippie.
Suddenly, an illegal oxygen generator explodes loudly in the luggage compartment, and the passenger cabin begins to fill with smoke. The cockpit door opens, and the pilot bursts into the compartment. "Gentlemen," he shouts, "I have good news and bad news. The bad news is that we're about to crash. The good news is that there are four parachutes, and I have one of them!" With that, the pilot throws open the door and jumps from the plane.
The venture capitalist immediately goes into action and says, "Gentlemen, I am the world's top venture capitalist, and probably the smartest man in the world. Obviously, I need a parachute." He grabs one, and out he jumps.
The Dalai Lama and the hippie look at one another. Finally, the Dalai Lama speaks, "My friend, I have lived a satisfying life and have known the bliss of True Enlightenment. You still have your life ahead of you, so you should take a parachute, and I'll go down with the plane."
The hippie smiles and said, "Hey, don't worry, your Holiness. The smartest man in the world just jumped out with my backpack."
Badaboom. What happens here is the reversal of power, that makes it funny.
Comic relief occurs when tension or suspense is broken with the use of humor. It's a device used by filmmakers in action or dramatic films, where tension is high, and humor is used to release the tension periodically, to cyclically drain the adrenaline glands. If the dramatic tension is kept at a solid 10 for two hours straight, the viewer becomes fatigued. Thus, the art of filmmaking is all about the careful control of dramatic cycles or waves, which are usually marked in acts and plot points. Comic relief is valuable for releasing tension periodically without resolving the core storyline. The textbook example of modern comic relief are C-3PO and R2-D2 in Star Wars, but the technique has been used since the time of Shakespeare.
Incongruity theory suggests that humor arises when logic and familiarity are replaced by things that don't normally go together. When a joke begins, our minds and bodies are already anticipating what's going to happen and how it's going to end. That anticipation takes the form of logical thought intertwined with emotion and is influenced by our past experiences and our thought processes. When the joke goes in an unexpected direction, this incongruity between the different parts of the joke as humorous.
An engineer, a Total Quality black belt, a programmer, and a true innovator were driving down a mountain in an old jeep when the brakes gave out. They screamed down the mountain, gaining speed, and finally managed to grind to a halt, more by luck than anything else, just inches from a thousand foot drop to jagged rocks. They all got out of the car.
The engineer says, "Pop the hood, I can fix this."
The Total Quality black belt says, "No, I think we should first convene a quality circle, do a pareto analysis and find an optimal solution before we use an adhoc approach."
The programmer says, "No, I think we should push it back up the hill and see if it does it again."
And the true innovator says, "Man, I just got an idea for a great amusement park ride!"
So which form of humor is best for ideation? Probably incongruity… because once you see the solution to a thorny problem was hidden in plain sight, you can't help but laugh. Superiority humor, especially if it is sarcastic or mean-spirited and used by senior management, it will certainly alienate the staff.
The Punchline of Life
Every month, new insights emerge to illuminate what lies behind the elusive human capacities for creativity. With time, this new science will develop into a powerful way of studying creativity, and will lead to new models for humor, creativity, and group ideation. However, neuroscience will not tell us everything we want to know about creativity. We cannot lose touch with the human meaning to all of this. We must remember that humor and creativity is all about making connections and expanding the meaning of our lives.
One more interesting finding from the gelotology is that on average, children laugh 400 times a day, while adults laugh about 15 times.[4] So as we age, we begin to lose our ability to be delighted. Researchers have indicated that the minimum number of laughs needed per day by adults is 30.[5] So maybe the goal isn't just to increase laughter in brainstormings, but to increase laughter in all of life.
Returning to the research of Rex Jung—that intellectual processing is fundamentally different from creativity, in which the neural pathways follow meandering paths—the good news is that even though our brains slowly lose the capacity to perform intellectual tasks as we age, the reason we lose that capacity—the covering that insulates neurons, called myelin, begins to gradually deteriorate—has a byproduct in that neural pathways begin to meander and wander, possibly in service of creative cognition. So as we get older and wiser, our ability to be creative and laugh about it all increases. And within this lies the punchline of life.
PS, below is one final offering, something to make any innovator laugh a little. If you do, try to feel your neural pathways shifting to enable greater creativity.
Source: © Moses Ma
This article reprinted by permission © 2014 FutureLabConsulting.com.
[1] Goleman, Daniel Jay, PhD. Emotional Intelligence. 84-86. NY: Bantam Books, 1995.
[2] Kudrowitz, Barry. M.I.T. PhD Thesis: Creativity, idea generation, improvisational humor, and product design. Ref: http://dspace.mit.edu/handle/1721.1/61610
[3] Dunn, Joseph R., PhD, Ed. New Discoveries in Psychoneuroimmunology. p 6-7.
[4] Palmer, Gary K. Brigham Young University. The Power of Laughter. p 32-35. Ensign, Sept 2007.
[5] Beck, Martha, PhD. The Joy Diet. p 160-162. NY: Crown Publishers, 2003.
Moses Ma, a partner at Next Gen Ventures, is co-author of the book Agile Innovation.
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There are few books that offer home cooks a new way to cook and to think about flavor—and fewer that do it with the clarity and warmth of Nik Sharma's Season. Season features 100 of the most delicious and intriguing recipes you've ever tasted, plus 270 of the most beautiful photographs ever seen in a cookbook. Here Nik, beloved curator of the award-winning food blog A Brown Table, shares a treasury of ingredients, techniques, and flavors that combine in a way that's both familiar and completely unexpected. These are recipes that take a journey all the way from India by way of the American South to California. It's a personal journey that opens new vistas in the kitchen, including new methods and integrated by a marvelous use of spices. Even though these are dishes that will take home cooks and their guests by surprise, rest assured there's nothing intimidating here. Season, like Nik, welcomes everyone to the table!


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Hercostomus acutilobatus är en tvåvingeart som beskrevs av Liao, Zhou och Yang 2006. Hercostomus acutilobatus ingår i släktet Hercostomus och familjen styltflugor. Inga underarter finns listade i Catalogue of Life.

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When Goldy Locks and Vince Russo get together—NOBODY IS SAFE!!! Just another Tuesday morning on The Brand where two of the MOST OPINIONATED PEOPLE ON THE PLANET give their views on everything going on in the world today!!!


This unique men's Canyon Outback Copper magnetic money clip features a magnet on the flap and inside main compartment to protect your credit cards. There's a magnetic clip for holding cash, inside slots to place credit cards and ID and outside slot for additional cards. It's constructed from full grain buffed cowhide leather making this a great gift idea for birthdays or holidays.


We recently placed a MyComputerCareer graduate into a Tier 1 Helpdesk position in Raleigh. This graduate came to us unemployed and feeling really defeated over his situation. He spent his time at MyComputerCareer focused on passing certification exams and learning how to capture a job. Although he made it to the final round of interviews the first two times out, the job went to someone else. Never deterred or discouraged, he began interviewing with another company and got his first IT job. With IT training from MyComputerCareer and the determination to succeed, he was able to launch his computer career!
Are you feeling defeated in your current employment situation? If so, and if you have the determination to make it in a new career, MyComputerCareer can help you obtain the knowledge and skills to begin your own IT career. MyComputerCareer has the program to get you started – regardless of your background. Take the FREE Career Evaluation today and get yourself moving towards a better life in a new career!


It's raining. That shouldn't come as a surprise seeing as this is the Pacific Northwest. However, they have had an unusually dry summer and this is the first rain in weeks. Given the chaotic nature of the past week, it's been a good opportunity to catch up on writing.
It's been a week since we arrived on Samish Island. When we first got here the weather was spectacular – dry and clear, but a bit warmer than we like. Through the week the smoke from the western first caught up with us, tainting the skies and coating everything with a nasty brown pall. Mountains that were visible earlier in the week disappeared, and at times we couldn't even see the other islands just a few miles across the bay. Our mood tended to deteriorate with the view.
We started by making multiple trips into town for provisions, including purchasing a new stove and dishwasher for the house. These will be delivered late next week, so for the time being we have to make do with our old stove and hand-washing dishes. We also made trips into town to get cable TV and Internet set up for the house. Each trip is a time-consuming affair. I started to see if ordering things from Amazon might be a more efficient way of getting what we need.
The biggest disruption, though, was with the house. First there was the septic system. Basically, the whole thing needed to be replaced. On Tuesday excavators arrived to dig up the front yard and install a new tank.
And, the one in these photos that they installed was the wrong one. They had to get this one out and go get the correct one.
In addition, there had to be electrical work to connect pumps, etc. The problem when you go poking into an old place like this is that if you start to pull at one thread, the whole thing could unravel. You don't want to go poking too hard. There were lots of things not up to code simply due to age. We're a bit worried about upcoming inspections.
Of course, the guy came to install our Internet connections just as the electrician had shut down power to the house. I improvised. I connected a power inverter to the Subaru and was able to pull enough power over a drop cord to power the modem. It worked.
With this morning's rain we found even more problems. Water came pouring in through the vent over the stove. The propane tank that heats the clothes dryer started leaking. Today's expedition into town included a search for roof sealant and a new tank. We got the new tank installed, and before martinis I crawled up on the roof and tried to patch the leaks. I guess we'll see how successful I was the next time it rains.
Even as we made new purchases and tried to get the house set up for our use for this year, it still seems like we're here only for a week or so. There are closets, workshops, nooks and crannies with all of the estate belongings. It will take a LONG time to sort it all out, and for now it's a bit overwhelming.
Finally, there were other concerns. With Hurricane Irma barreling in we were worried about family in Florida. There were multiple phone calls, making sure that everyone had found a place to ride out the storm. We hope for continued safety for all of them through this weekend as the storm makes landfall.
So that's where we are right now. Things are slowly coming together, and we hope that we can fall into a normal routine.


text:
By Janene Pieters on January 23, 2019 - 15:10
Resuscitation Photo: photographee.eu/DepositPhotos
Dieredik van Dijk, professor of intensive care at UMC Utrecht, spoke to a number of resuscitated patients who later decided it was not what they wanted. Due to the stress or time pressure in the moment, patients often can't make an informed decision, he said to the newspaper. It is therefore necessary to talk and think about resuscitation before you are in an emergency situation, Van Dijk, the Patient Federation and ANBO said. This is especially true for people who are at a higher risk of dying due to their age or health issues. People can discuss a Do Not Resuscitate order with their house doctor, or at a clinic.
"In principle this call is for everyone, because it can happen to anyone that you suddenly end up in an emergency room", Liane den Haan, director of ANBO, said to NOS. "But it naturally involves mainly elderly and vulnerable people, or already ill. It is very important that they think about this." Older people have to decide what they want, Den Haan said. "Otherwise their families have to do it. That is difficult if it was never discussed."
"It is time for an awareness campaign", Thom Meens of the Dutch Patient Federation said to AD. According to him, people prefer not to think about the last phase of their lives. "If you are in the emergency room, you are actually already too late. Because the conversation is so difficult, you have to have it with a trusted counselor: your GP, because he also knows your home situation." Meens also said that this call is mainly for the elderly. "Think about it when you notice that you are deteriorating. For most people, this is roughly between 70 and 80 years. The moment you think about things like 'who should handle my finances if I can not do it anymore?', then it is also time to think about resuscitation at the end of life."
The Patient Federation teamed up with a number of GPs to publish an information leaflet about DNRs. This will eventually be available through all GPs. Though the national family practice association LHV could not tell AD whether all GPs are actively talking to patients about resuscitation. "We do not have figures, but more and more GPs are conducting these conversations. This is also a logical consequence of the growing group of elderly patients in general practice", a spokesperson said to the newspaper.
Patient Federation
Dieredik van Dijk
Liane den Haan
Thom Meens


Sports executives, sometimes known as team presidents, CEOs, and general managers, oversee the business operations of professional, collegiate, and minor league sports teams. They are responsible for the teams' finances, as well as overseeing the other departments within the organization, such as marketing, public relations, accounting, ticket sales, advertising, sponsorship, and community relations. Sports executives also work on establishing long-term contacts and support within the communities where the teams play.


Cotaplan were tasked with creating a Children and Families centre at Southmead Primary School in London.
With limited access for transport and crane works the delivery of this project needed to be carefully planned from the outset. With the site restrictions presented the decision was made to construct a new flat pack building system to create a Children & Families Centre. The flat pack system ensured the weight of each unit was kept to a minimum lift size required due to the site restrictions. The flat pack system also ensured that our client received the best building system available for achieving a traditional finish both internally and externally.
The works consisted of a full turnkey package inclusive of a new flat pack building system, foundations, drainage, service connections, external works and landscaping.
To achieve a traditional appearance the external finish of Rockclad was specified together with incorporating a range of internal finish associated with traditional methods of construction..
The centre was completed on time and on budget.


GizmoWatch is the grinding mill that constantly tracks pulse of all the latest gadgets, cool gadgets, gizmos, electronics and technology news. Call it our passion, charm or craze – all we boil down to is just one thing – the must-have gadgets and technology that make gadgets go. Whether it's from a convenience point of view or for its sheer stylish look, if it's the latest buzz in gadgets, it's definitely going to find place here. At GizmoWatch, we aim at providing you in-depth reviews, with pricing and competition, of latest gadgets launched around the world on each passing day. We also make lists and guides to help you decide what you should own and what you shouldn't, all this in the simplest and the easiest way so that even the novice can understand and gel with us.
We are looking out for some enthusiastic people to work with us and who could prove to be an asset with their knowledge and skill. So are you ready to make a dent in the web world?


We are building a dynamic, passionate team of professionals. Whether you are new to the Medical field or a current professional, our Specimen Accessioners are building a foundation of success.
As a part of the LabCorp Accessioning team, you can be a part and be connected to something amazing. Delivering World Class Diagnostics, Bringing Innovative Medicines to Patients Faster and Changing the Way Care is Provided is the LabCorp Strategy!
Unpack specimens from branches or ports and routes specimens by type to various staging areas.
Prepare all specimens received for testing in designated laboratory departments or locations such as staging of specimens, centrifuge, separate serum, and blood smears.
Prepare excess specimen samples for storage and resolves and document problem specimens.
Career Growth: Specimen Accessioners are encouraged and developed to grow into Team Leaders, Lab Managers and Lab Supervisors.
Proven data entry experience. A majority of time spent in this position will be performing data entry.
Attention to detail and critical thinking skills.
Ability to read and understand complex directions.
Ability to follow lab safety practices when working with hazardous materials.
Ability to work in a fast paced, multi-tasking environment and maintain production and quality standards determined by the clinical laboratory.


Beate Beime Pharma Consulting assists in drug development and the complete approval process for medicinal products including readability user testing, thus ensuring that your products gain access to the market.
We bring nearly 20 years of experience in drug development and the registration process for medical products, thus ensuring that your products gain access to the market.
The proof of efficacy and safety of your product requires an intelligent strategy that complies with regulatory directives, as well as professional management of clinical studies (clinical trials) and careful documentation for the relevant filing during each phase of implementation.
We conduct a readability test of the package information leaflet by an interview procedure. The test methods validated and standardized by Beate Beime ensure reliable and, above all, fast results – important for drugs in the final phase of the approval process. We also support you with the realisation of Usability Testing.


text:
IAI Certified to Convert Boeing 737-800 into Cargo Plane
The approval comes as the demand for cargo flights, which are crucial for the delivery of supplies and equipment, has been rising due to the COVID-19 crisis. IAI's Aviation Group has already delivered the first two converted aircraft
IsraelDefense | 7/04/2020
Photo:IAI
Israel Aerospace Industries (IAI) announced on April 6 that it has been certified by the US Federal Aviation Administration and the Civil Aviation Authority of Israel to convert Boeing's 737-800 passenger aircraft into a cargo jet.
IAI, Israel's largest aerospace and defense company, is the only company to convert both the 737-700 and the 737-800 of Boeing into a cargo configuration. IAI's Aviation Group has already delivered the first two converted B737-800 aircraft.
With the COVID-19 crisis forcing many airlines into halting passenger service, the demand for cargo flights, which are crucial for the delivery of medical supplies, food, and other necessary equipment, has been rising.
The Aviation Group was founded in January 2019 when all of IAI's activities involving manned aircraft, both military and civilian, were consolidated into a single business unit. It is one of the few business operations in the world that specializes in converting passenger aircraft into cargo configurations. The Group handles both wide-body and narrow-body aircraft, which are operated by some of the world's largest shipping companies such as Amazon and DHL.
Yossi Melamed, IAI's EVP and general manager of the Aviation Group, said, "IAI is excited to receive the FAA's certification for converting B737-800s, and we thank both the FAA and the CAAI. We have witnessed increased demand for cargo aircraft in recent years."
"Being able to convert additional models will help us meet the demand. I would like to thank our partners at the Haite Group in China for their trust in IAI. In addition, IAI sends our best wishes to all airlines impacted by the COVID-19 crisis, and hope they will resume all their flights soon."
According to the company, IAI specializes in developing and manufacturing advanced, state-of-the-art systems for air, space, sea, land, cyber and homeland security. It provides advanced technology solutions to government and commercial customers worldwide, designs and manufactures business jets and aerostructures, performs overhaul and maintenance on commercial aircraft, and converts passenger aircraft to refueling and cargo configurations.
Leaders wave after the signing of the Abraham Accords at the White House, September 2020. Photo: REUTERS/Tom Brenner
United front against Iran: Israel added to countries under US Central Command
The Pentagon says "The easing of tensions between Israel and its Arab neighbors subsequent to the Abraham Accords has provided a strategic opportunity for the United States to align key partners against shared threats in the Middle East"
Mandi Kogosowski | 17/01/2021
Rafael demonstrates advanced tactical radio, sensor-to-shooter capabilities to German Army
US Army's future battle command system cleared for production
Dutch Special Forces to receive new shooting ranges
Carbyne pulls in $25 mil for emergency communications platform development


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Home / Sports / Hometown Oceanside Team Wins National Beach Soccer Championship
2015 National Beach Soccer Champions SoCal Legacy, from left to right: Coach Steve Citron, Mateo Citron, Lars Ecklund, James Pullara, Andrew Torres, Connor Gillespie, Israel Ramirez, Juan Nava, Eiko Rodriguez, Hayden Morrison, Jimmy Cruz, and Assistant Coach Enrique Nava
Hometown Oceanside Team Wins National Beach Soccer Championship
in Sports December 16, 2015
Clearwater FL— SoCal Legacy BFC defeated GFL Soccer Enterprises 5-1 to win the Major Beach Soccer BU14 National Championships at Clearwater Beach, Florida on Sunday, December 13, 2015.
With over 50 tournament matches worth of experience, nearly a dozen local championship wins, and countless hours of practice, SoCal Legacy's Oceanside-based homegrown talent traveled to Florida to compete in the 2-day event, and were the only team in their bracket that went undefeated in the preliminary matches and final stages, as they claimed victory over local Floridian favorites such as Kicks, hailing from West Palm Beach, by a score of 7-4, and the Savages, from Bradenton, Florida, 6-3.
The match against the Savages was challenging, but their attempt to make a comeback early in the third period was defused by an amazing bicycle kick goal, scored by Eiko Rodriguez, which completely eliminated any hopes for the Savages to catch up to the "boys from Oceanside" who were on their way to the championship rounds. The picture perfect goal was assisted by goalie Jimmy Cruz, who made a perfect height throw, deep into Savage territory, which Eiko shot first time, in mid-air, into the back of the net. Known for his prolific goal scoring capabilities, by the end of the tournament Eiko had amassed 10 of the team's 24 goals.
The next match was the highly anticipated contest between Legacy and GFL Soccer Enterprises (GFLSoccer.com) out of St. Petersburg, Florida. "We researched the competitors prior to our Florida departure", said SoCal Legacy Coach Steve Citron, "and we noticed that GFL has strong relationships with various professional teams in the German Bundesliga and they routinely fly their youth players and teams over to Europe to train, try-out, and play against Academy teams from Bayern Munich and other cities throughout Germany.
To date, they have had 12 youth players from their club try out for professional teams and, this year, Stevie Rudderham was the first GFL player who signed with FC Magdeburg, and he is now playing in Germany. With all of this European influence, combined with the fact that GFL also intertwines beach soccer training into their traditional soccer programs, well, we anticipated that they would be the team to beat."
In the third pool-play match of the tournament Legacy took an early lead against GFL, but the German-coached team from St. Petersburg battled back to stay within striking distance. Then Legacy scored a flurry of goals in the third period including a beautiful and powerful header from distance by Israel Ramirez to take the win by a score of 6-3. "The competition was so tight that we could have had a 3-way tie for first place, had we lost that match, at which point they would have decided the two finalist by tiebreaker rules, and we had simply traveled too far to risk falling short of the final, so I told the team it was a must-win", added Coach Citron.
After their three decisive wins, Legacy moved into the championship match, but there was a 3-way tie for second place after the completion of the preliminary pool-play matches, so the second team to advance to the final was decided by goal differential. GFL once again emerged as the contender to take on Oceanside's own SoCal Legacy in the final, and the stage was set for an incredible re-match.
Before the whistle blew for the start of the BU14 National Championship, Coach Citron urged the team to weather the storm and that GFL would come out strong with "everything they have" for the first half of the contest to try to secure an early lead, but that their energy level would eventually fade against the intensely trained Oceanside players. "We have been playing beach soccer as a team for three years and this year we maintained our training regime, after the spring and summer beach season, to prepare for this national competition", Citron stated, "so our team can literally play for hours on the sand without slowing down."
The first period was extremely competitive with both teams having significant goal scoring opportunities, but the boys from O'side pulled ahead 2-0, with goals from both Eiko and Israel respectively, while holding their opponents scoreless through the end of the first period.
But the game was far from over as GFL pushed hard towards equalizing by scoring a goal within the first 30 seconds of the second period. The action went back and forth and, as that period came to a close, Legacy was barely holding onto a narrow 2-1 lead. In the event of a tie, the match would go to a 3-minute golden goal overtime period followed by penalty kicks. "We did not want to go there, and had noticed GFL was beginning to look really tired at the end of the second period", Citron stated.
With the third and final 10-minute period left to go, and only a one goal differential on the scoreboard, it was anyone's game, but during the first few minutes of the period Legacy began to leverage their training and fitness advantage. As their opponents began to slow down, Legacy continued forward, looking for the right opportunity to strike. Then suddenly, midway through the third period, Israel scored again with what appeared to be an impossible shot from an incredible side-angle to begin building on the team's lead.
Photos and story continued on Page 2
Beach Soccer Clearwater Beach National Championships Oceanside SoCal Legacy BFC	2015-12-16
Tagged with: Beach Soccer Clearwater Beach National Championships Oceanside SoCal Legacy BFC


BTW, I also use lisp.
Was it - x or +x?
BTW, my van used arch.
It has a potential to become an exploitable, what do you guys think?
Doing everything in the shell!
Linu(x/s)... there's something I've noticed.
When you tell everyone that you use arch.
The only reason I never dual boot Windows and Linux!!
M$ is for capitalist bootlickers.
finally, i can run an electron app!
Pretty sure this belongs here. Joy thinks that distros have to make money.
It's almost too late for this one. Good riddance.
Who Wants To Help Me Fund My New Distro?


The use of nanosatellites for space missions is only at its beginning. They are seen as possible replacements for some of the more costly missions now conducted by traditional satellites. We share the same belief and we have noticed recently that important players in the aerospace domain are starting to focus their attention on this new sector.
One particular development generating considerable attention and funding is directed at using nanosatellites as platforms for distributed data acquisition. Satellites can be either locally distributed – formation flying – or can cover larger areas in a constellation-like configuration depending on the specific nature of the phenomenon that presents interest (local or wide area fluctuations of the properties need to be monitored). One step forward is the utilization of these distributed spacecrafts as nodes in a distributed processing system where all satellites are connected in a mobile ad-hoc network sharing their resources for solving complex tasks and relaying not raw data, but partially or completely computed data to the ground stations. Such a modular system has another advantage in the reduced manufacturing cost for a series of nanosatellites when compared with the manufacturing of a conventional big satellite having the same functions. Moreover one has to take into account that the increased reliability of the complete system that will continue to execute all the assigned tasks even if part of the nanosatellites composing it malfunction.
A second application type employs nanosatellites as a testbed for space qualification of hardware that never performed on orbit. In-flight testing can be implemented on board nanosatellites at similar costs with ground testing, but with more accurate environmental conditions and, consequently, with better estimates on the system's reliability. Implementation is possible for estimating the space influence on real size subsystems or scaled down models. Also nanosatellites can be used to visually inspect each other or larger satellites to determine effects caused by impact with space debris or micrometeorites.
A related development field targets the use of nanosatellites to validate models and algorithms used in physical modeling of the spacecrafts and the near earth environment. Attitude and orbit control laws and specific algorithms can also be evaluated first on nanosatellites to detect possible problems before the implementation on a larger and very expensive satellite.
All this possible developments are the focus of our future research projects and GOLIAT represents only the initial step in the direction of developing complex space applications using nanosatellites.


text:
from django.contrib.auth.mixins import UserPassesTestMixin
from django.shortcuts import get_object_or_404

from grandchallenge.teams.models import Team, TeamMember

class UserIsTeamOwnerOrChallengeAdminMixin(UserPassesTestMixin):
    def test_func(self):
        challenge = self.request.challenge
        team = get_object_or_404(Team, pk=self.kwargs["pk"])
        return (self.request.user == team.owner) or challenge.is_admin(
            self.request.user
        )

class UserIsTeamMemberUserOrTeamOwnerOrChallengeAdminMixin(
    UserPassesTestMixin
):
    def test_func(self):
        challenge = self.request.challenge
        team_member = get_object_or_404(TeamMember, pk=self.kwargs["pk"])
        return (
            (self.request.user == team_member.user)
            or (self.request.user == team_member.team.owner)
            or challenge.is_admin(self.request.user)
        )

class UserIsChallengeParticipantOrAdminMixin(UserPassesTestMixin):
    def test_func(self):
        user = self.request.user
        challenge = self.request.challenge
        return challenge.is_admin(user) or challenge.is_participant(user)

redpajama_set_name: RedPajamaGithub